Chapter Exam

Chapter-11 Similarity and Congruence — Online MCQ Test

Q: Two triangles are congruent. Which of the following is NOT a sufficient condition for congruence?

Answer: C. AAA (Angle-Angle-Angle) — AAA proves similarity, not congruence. Two triangles with equal angles can have different sizes. SSS, SAS, and RHS all guarantee congruence.

Q: Two similar triangles have corresponding sides in the ratio 2:5. If the smaller triangle has a perimeter of 24 cm, what is the perimeter of the larger triangle?

Answer: A. 60 cm — The perimeter scales by the same factor as the sides. If sides are in ratio 2:5, then perimeters are also in ratio 2:5. Therefore, 24 × (5/2) = 60 cm.

Q: Two cubes have a linear scale factor of 2:3. The smaller cube has a volume of 64 cm³. What is the volume of the larger cube, and by what factor does the volume increase?

Answer: B. 216 cm³; factor of 3.375 — Linear scale factor 2:3 means volume scale factor is (2:3)³ = 8:27. Volume of larger cube = 64 × (27/8) = 216 cm³. The volume increases by factor 27/8 = 3.375.

MATHS · Grade 10 · IGCSE cambridge

Practice Chapter-11 Similarity and Congruence with a free chapter-wise online MCQ test for IGCSE cambridge Grade 10 MATHS. This chapter covers: Similar shapes scale factors for length area and volume and conditions for congruent triangles.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-11 Similarity and Congruence — Important Questions & Answers (FAQ)

Frequently asked questions from IGCSE cambridge Grade 10 MATHS — Chapter-11 Similarity and Congruence, with answers and explanations. These are sample questions; the exam has its own separate question set.

Two triangles are congruent. Which of the following is NOT a sufficient condition for congruence?

A. SSS (Side-Side-Side)
B. SAS (Side-Angle-Side)
C. AAA (Angle-Angle-Angle) ✓
D. RHS (Right angle-Hypotenuse-Side)

Answer: C. AAA (Angle-Angle-Angle)
AAA proves similarity, not congruence. Two triangles with equal angles can have different sizes. SSS, SAS, and RHS all guarantee congruence.

What does a scale factor of 2 mean when comparing two similar shapes?

A. All linear dimensions of the larger shape are twice those of the smaller shape ✓
B. The area of the larger shape is twice that of the smaller shape
C. The perimeter is half of the original
D. The volume increases by a factor of 2

Answer: A. All linear dimensions of the larger shape are twice those of the smaller shape
A scale factor of 2 for length means all linear dimensions (sides, heights, widths) are multiplied by 2. Area scales by 2², and volume by 2³.

Two similar triangles have corresponding sides in the ratio 2:5. If the smaller triangle has a perimeter of 24 cm, what is the perimeter of the larger triangle?

A. 60 cm ✓
B. 48 cm
C. 96 cm
D. 120 cm

Answer: A. 60 cm
The perimeter scales by the same factor as the sides. If sides are in ratio 2:5, then perimeters are also in ratio 2:5. Therefore, 24 × (5/2) = 60 cm.

Which of the following is a condition that guarantees congruence of two right-angled triangles?

A. Two angles are equal
B. One leg and the hypotenuse are respectively equal to one leg and hypotenuse of the other triangle ✓
C. The hypotenuses are equal
D. Two legs are equal in length

Answer: B. One leg and the hypotenuse are respectively equal to one leg and hypotenuse of the other triangle
The RHS (Right angle-Hypotenuse-Side) condition states that if the hypotenuse and one leg of a right triangle equal the hypotenuse and one leg of another right triangle, they are congruent.

Two cubes have a linear scale factor of 2:3. The smaller cube has a volume of 64 cm³. What is the volume of the larger cube, and by what factor does the volume increase?

A. 144 cm³; factor of 1.5
B. 216 cm³; factor of 3.375 ✓
C. 192 cm³; factor of 2.25
D. 288 cm³; factor of 4.5

Answer: B. 216 cm³; factor of 3.375
Linear scale factor 2:3 means volume scale factor is (2:3)³ = 8:27. Volume of larger cube = 64 × (27/8) = 216 cm³. The volume increases by factor 27/8 = 3.375.